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Stabilization of second order evolution equations with unbounded feedback with delay

Published online by Cambridge University Press:  21 April 2009

Serge Nicaise  and
Julie Valein
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, 59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Julie.Valein@univ-valenciennes.fr
Julie Valein
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, 59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Julie.Valein@univ-valenciennes.fr
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Abstract

We consider abstract second order evolution equations with unbounded feedback with delay. Existence results are obtained under some realistic assumptions. Sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability. Some new examples that enter into our abstract framework are presented.

Keywords

Second order evolution equationswave equationsdelaystabilization functional
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 2 , April 2010 , pp. 420 - 456
Copyright
© EDP Sciences, SMAI, 2009

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